It is already known that a composite substrate, in which a supporting substrate and a piezoelectric substrate are bonded together, is provided with electrodes to fabricate elastic wave devices. For example, as elastic wave devices, surface acoustic wave devices and bulk acoustic wave devices have been used as band-pass filters in communication devices, such as mobile phones. Composite substrates are known to use lithium niobate or lithium tantalate as a piezoelectric substrate and silicon or quartz as a supporting substrate (see Patent Document 1).    [Patent Document 1] Japanese Unexamined Patent Application Publication No. 2006-319679
Such composite substrates are often manufactured by preparing a piezoelectric substrate and a supporting substrate, bonding the piezoelectric substrate to the supporting substrate with an organic adhesive layer interposed therebetween, and reducing the thickness of the piezoelectric substrate. Since an edge of a substrate may hit something and be broken during handling, a piezoelectric substrate is generally beveled. When the thickness of a piezoelectric substrate is decreased, abrasive grains are placed between a surface of a piezoelectric substrate and a lapping plate, and the surface of the piezoelectric substrate is lapped with the lapping plate. However, according to such a manufacturing method, when a piezoelectric substrate and a supporting substrate are bonded together, an organic adhesive layer is not fully applied up to a beveled edge of the piezoelectric substrate. Furthermore, since beveling increases the distance between the piezoelectric substrate and the supporting substrate, an edge of the piezoelectric substrate is not bonded to the supporting substrate. In such a state, lapping of the surface of the piezoelectric substrate with a lapping plate causes a problem of frequent occurrence of chipping from the edge.